1349_Wormholes

While exploring his many farms, Farmer John has discovered a number of amazing wormholes. A wormhole is very peculiar because it is a one-way path that delivers you to its destination at a time that is BEFORE you entered the wormhole! Each of FJ's farms comprises N ( 1 ≤ N ≤ 500) fields conveniently numbered 1..N, M ( 1 ≤ M ≤ 2500 ) paths, and W ( 1 ≤ W ≤ 200 ) wormholes.

As FJ is an avid time-traveling fan, he wants to do the following: start at some field, travel through some paths and wormholes, and return to the starting field a time before his initial departure. Perhaps he will be able to meet himself :) .

To help FJ find out whether this is possible or not, he will supply you with complete maps to F ( 1 ≤ F ≤ 5 ) of his farms. No paths will take longer than 10,000 seconds to travel and no wormhole can bring FJ back in time by more than 10,000 seconds.

Line 1:     A single integer, F. F farm descriptions follow.

Line 1 of each farm:    Three space-separated integers respectively: N, M, and W

Lines 2..M+1 of each farm:    Three space-separated numbers (S, E, T) that describe, respectively: a bidirectional path between S and E that requires T seconds to traverse. Two fields might be connected by more than one path.

Lines M+2..M+W+1 of each farm:     Three space-separated numbers (S, E, T) that describe, respectively: A one way path from S to E that also moves the traveler back T seconds.

Lines 1..F:   For each farm, output "YES" if FJ can achieve his goal, otherwise output "NO" (do not include the quotes).

2
3 3 1
1 2 2
1 3 4
2 3 1
3 1 3
3 2 1
1 2 3
2 3 4
3 1 8

NO
YES

For farm 1, FJ cannot travel back in time.

For farm 2, FJ could travel back in time by the cycle 1 -> 2 -> 3 -> 1, arriving back at his starting location 1 second before he leaves. He could start from anywhere on the cycle to accomplish this.